A new substance is developed in a laboratory and has the following properties: normal melting point, \(83.7^{\circ} \mathrm{C}\); normal boiling point, \(177^{\circ} \mathrm{C}\); triple point,200 Torr and \(38.6^{\circ} \mathrm{C}\). (a) Sketch the approximate phase diagram and label the solid, liquid, and gaseous phases and the solid-liquid, liquid-gas, and solid-gas phase boundaries. (b) Sketch an approximate cooling curve for a sample at constant pressure, beginning at 500 Torr and \(25^{\circ} \mathrm{C}\) and ending at \(200^{\circ} \mathrm{C}\).

The melting point of a substance is the temperature at which it changes from a solid to a liquid. This is a key feature in the study of matter as it signifies a phase transition. For the substance described in the exercise, the melting point is given as an exact temperature, 83.7°C under normal atmospheric pressure. At this point, the molecules within the solid substance have enough energy to overcome their fixed positions and start to move freely, resulting in the solid becoming a liquid. The melting point can also be influenced by pressure, but in this case, we refer to the 'normal' melting point at 1 atmosphere (atm) of pressure.

Understanding melting points is crucial for applications such as determining the purity of a substance since impurities can alter the melting point. In the context of a phase diagram, the melting point is where the line that separates solid and liquid phases meet at a specific pressure, usually 1 atm for a 'normal' melting point.

The boiling point is another significant temperature in the study of matter, identifying the moment when a liquid changes to a gas. The exercise states a 'normal boiling point' for the new substance at 177°C. As with the melting point, this temperature is specific to a pressure of 1 atm. At the boiling point, the vapor pressure of the liquid equals the external pressure, allowing bubbles of vapor to form within the liquid leading to boiling.

Boiling points help us to understand the energy required for a liquid to become a gas and can be used to compare the volatility of different substances. On a phase diagram, the boiling point is represented by the point where the liquid-gas boundary line crosses the 1 atm pressure line.

The triple point is a unique condition where a substance's solid, liquid, and gaseous phases coexist in equilibrium. For the substance in the exercise, it's given as 200 Torr and 38.6°C. This point is significant because it’s the only set of conditions under which all three phases can be present at the same time. In the phase diagram, the triple point is where all three phase boundary lines converge.

Triple points are pivotal in the calibration and definition of temperature scales. They also provide valuable information about the substance's properties, such as whether sublimation (direct solid-to-gas transition) is possible at certain pressure levels.

A cooling curve represents the change in temperature of a substance over time as it cools and undergoes phase transitions at constant pressure. For the exercise's substance, the curve would begin at 500 Torr and 25°C and end at 200°C. It's an approximate graphical representation that indicates how the temperature falls and plateaus as the material changes from gas to liquid, and finally to solid, if cooled sufficiently below its melting point.

Each plateau on the cooling curve corresponds to a phase change, where the temperature remains constant while the phase transition occurs. Understanding and interpreting cooling curves are fundamental when studying a substance's thermal properties and behavior during cooling.

Matter states, commonly known as phases of matter, include solids, liquids, and gases, which differ in their properties due to the varying arrangement and movement of atoms or molecules. Solids have fixed shapes and volumes; liquids have fixed volumes but take the shape of their containers; gases have neither fixed volume nor shape and will expand to fill their containers.

These states are influenced by temperature and pressure, which can change the state of a substance through a process known as a phase transition. These transitions, including melting, freezing, vaporization, condensation, and sublimation, are fundamental concepts in chemistry and physics, helping us to understand how substances interact with environmental conditions.

Phase transitions are the transformations between different states of matter. They occur when energy, in the form of heat, is either absorbed or released by a substance, thereby changing its physical state. Common phase transitions include melting (solid to liquid), freezing (liquid to solid), vaporization (liquid to gas), condensation (gas to liquid), and sublimation (solid to gas).

Each transition requires energy changes: endothermic processes absorb heat, like melting and vaporization, while exothermic processes release heat, such as freezing and condensation. Phase transitions are characterized by temperature plateaus during heating or cooling, where energy changes state without altering temperature. This concept is vital for interpreting phase diagrams and understanding the thermodynamic behavior of substances.